# LQG Graphon Mean Field Games: Analysis via Graphon Invariant Subspaces

arXiv: https://arxiv.org/abs/2004.00679 · HTML: https://mlsanity.com/paper/2004.00679/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2020.

## Built on by (most cited first, 4 of 4)

- [Policy Optimization for Continuous-time Linear-Quadratic Graphon Mean Field Games](https://mlsanity.com/paper/2506.05894/) (2025)
- [Fixed-Point Centrality for Networks](https://mlsanity.com/paper/2209.07070/) (2022)
- [Graphon Particle Systems, Part II: Dynamics of Distributed Stochastic Continuum Optimization](https://mlsanity.com/paper/2407.02765/) (2024)
- [Data-Driven Network LQG Mean Field Games with Heterogeneous Populations via Integral Reinforcement Learning](https://mlsanity.com/paper/2602.14339/) (2026)

## Abstract (arXiv)

This paper studies approximate solutions to large-scale linear quadratic stochastic games with homogeneous nodal dynamics parameters and heterogeneous network couplings within the graphon mean field game framework in [2]-[4]. A graphon time-varying dynamical system model is first formulated to study the finite and then limit problems of linear quadratic Gaussian graphon mean field games (LQG-GMFG). The Nash equilibrium of the limit problem is then characterized by two coupled graphon time-varying dynamical systems. Sufficient conditions are established for the existence of a unique solution to the limit LQG-GMFG problem. For the computation of LQG-GMFG solutions two methods are established and employed where one is based on fixed point iterations and the other on a decoupling operator Riccati equation; furthermore, two corresponding sets of solutions are established based on spectral decompositions. Finally, a set of numerical simulations on networks associated with different types of graphons are presented.